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Nonequilibrium Phase Transitions to Collective Behavior in Stochastic Spatially Extended Systems

2007
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Release : 2007
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Book Rating : 020/5 ( reviews)

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Book Synopsis Nonequilibrium Phase Transitions to Collective Behavior in Stochastic Spatially Extended Systems by : Kevin B. Wood

Download or read book Nonequilibrium Phase Transitions to Collective Behavior in Stochastic Spatially Extended Systems written by Kevin B. Wood. This book was released on 2007. Available in PDF, EPUB and Kindle. Book excerpt: We explore nonequilibrium collective behavior in large, spatially extended stochastic systems. In Part I, we present a model of discrete, active, noisy phase oscillators sufficiently simple to be characterized in complete detail in a host of diverse settings. In Chapter 2, we introduce the model and detail its utility for the study of both continuous and discontinuous phase transitions to macroscopic oscillations. In Chapter 3 we analyze a locally coupled version of the model undergoing a continuous transition and provide strong evidence that the inherently nonequilibrium system shows qualitative and quantitative characteristics of a known class of equilibrium phase transitions. Chapter 4 offers an analysis of the discrete model in the face of quenched transition rate disorder, where synchronization still occurs and depends on the degree of disorder in the population. The final chapter of Part I, Chapter 5, details the microscopic underpinnings of synchronization above threshold, including the counterintuitive relationship between time-averaged frequency and the mean field oscillations. The second part of the dissertation begins with an introduction to generic relaxational models with field-dependent kinetic coeffcients, highlighting in particular the role of this class of models in the study of noise-induced phase transitions. Using these systems as prototypical models of noise-induced phenomena in spatially extended systems, we offer a comprehensive study of static pattern formation in Chapter 7, while Chapter 8 provides a numerical study of coherent oscillatory dynamics induced purely by noise. Finally, Chapter 9 details an analytical framework for studying the dynamics of these systems which is capable of approximately describing both static and time-dependent phases associated with the nonequilibrium transitions in these relaxational models.

Universality In Nonequilibrium Lattice Systems: Theoretical Foundations

2008-05-08 Science
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Release : 2008-05-08
Genre : Science
Kind : eBook
Book Rating : 305/5 ( reviews)

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Book Synopsis Universality In Nonequilibrium Lattice Systems: Theoretical Foundations by : Geza Odor

Download or read book Universality In Nonequilibrium Lattice Systems: Theoretical Foundations written by Geza Odor. This book was released on 2008-05-08. Available in PDF, EPUB and Kindle. Book excerpt: Universal scaling behavior is an attractive feature in statistical physics because a wide range of models can be classified purely in terms of their collective behavior due to a diverging correlation length. This book provides a comprehensive overview of dynamical universality classes occurring in nonequilibrium systems defined on regular lattices. The factors determining these diverse universality classes have yet to be fully understood, but the book attempts to summarize our present knowledge, taking them into account systematically.The book helps the reader to navigate in the zoo of basic models and classes that were investigated in the past decades, using field theoretical formalism and topological diagrams of phase spaces. Based on a review in Rev. Mod. Phys. by the author, it incorporates surface growth classes, classes of spin models, percolation and multi-component system classes as well as damage spreading transitions. (The success of that review can be quantified by the more than one hundred independent citations of that paper since 2004.)The extensions in this book include new topics like local scale invariance, tricritical points, phase space topologies, nonperturbative renormalization group results and disordered systems that are discussed in more detail. This book also aims to be more pedagogical, providing more background and derivation of results. Topological phase space diagrams introduced by Kamenev (Physical Review E 2006) very recently are used as a guide for one-component, reaction-diffusion systems.

Renormalization Group Analysis of Nonequilibrium Phase Transitions in Driven Disordered Systems

2019-01-24 Science
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Release : 2019-01-24
Genre : Science
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Book Rating : 711/5 ( reviews)

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Book Synopsis Renormalization Group Analysis of Nonequilibrium Phase Transitions in Driven Disordered Systems by : Taiki Haga

Download or read book Renormalization Group Analysis of Nonequilibrium Phase Transitions in Driven Disordered Systems written by Taiki Haga. This book was released on 2019-01-24. Available in PDF, EPUB and Kindle. Book excerpt: This book investigates phase transitions and critical phenomena in disordered systems driven out of equilibrium. First, the author derives a dimensional reduction property that relates the long-distance physics of driven disordered systems to that of lower dimensional pure systems. By combining this property with a modern renormalization group technique, the critical behavior of random field spin models driven at a uniform velocity is subsequently investigated. The highlight of this book is that the driven random field XY model is shown to exhibit the Kosterlitz–Thouless transition in three dimensions. This is the first example of topological phase transitions in which the competition between quenched disorder and nonequilibrium driving plays a crucial role. The book also includes a pedagogical review of a renormalizaion group technique for disordered systems.

Non-Equilibrium Phase Transitions

2008-11-27 Science
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Release : 2008-11-27
Genre : Science
Kind : eBook
Book Rating : 659/5 ( reviews)

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Book Synopsis Non-Equilibrium Phase Transitions by : Malte Henkel

Download or read book Non-Equilibrium Phase Transitions written by Malte Henkel. This book was released on 2008-11-27. Available in PDF, EPUB and Kindle. Book excerpt: This book describes two main classes of non-equilibrium phase-transitions: static and dynamics of transitions into an absorbing state, and dynamical scaling in far-from-equilibrium relaxation behavior and ageing.

Collective Dynamics of Nonlinear and Disordered Systems

2005-11-02 Science
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Release : 2005-11-02
Genre : Science
Kind : eBook
Book Rating : 693/5 ( reviews)

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Book Synopsis Collective Dynamics of Nonlinear and Disordered Systems by : Günter Radons

Download or read book Collective Dynamics of Nonlinear and Disordered Systems written by Günter Radons. This book was released on 2005-11-02. Available in PDF, EPUB and Kindle. Book excerpt: Phase transitions in disordered systems and related dynamical phenomena are a topic of intrinsically high interest in theoretical and experimental physics. This book presents a unified view, adopting concepts from each of the disjoint fields of disordered systems and nonlinear dynamics. Special attention is paid to the glass transition, from both experimental and theoretical viewpoints, to modern concepts of pattern formation, and to the application of the concepts of dynamical systems for understanding equilibrium and nonequilibrium properties of fluids and solids. The content is accessible to graduate students, but will also be of benefit to specialists, since the presentation extends as far as the topics of ongoing research work.

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